Problem Description

E869120 is trying to create an emblem on a 2D plane using $N + M$ circles numbered $1, 2, 3, \cdots, N + M$ to commemorate the holding of square869120Contest #5.
The circles numbered $1, 2, 3, \cdots, N$ have fixed center coordinates $(x_i, y_i)$ and radii $r_i$.
On the other hand, the circles numbered $N + 1, N + 2, N + 3, \cdots, N + M$ have fixed center coordinates $(x_i, y_i)$ but their radii are not determined.
The circles used in the emblem may touch each other, but no circle should intersect or contain another circle. Maximize the radius of the smallest circle.

Input Format

The input is given from the standard input in the following format:

$N$ $M$ $x_1$ $y_1$ $r_1$ $x_2$ $y_2$ $r_2$ $:$ $:$ $x_N$ $y_N$ $r_N$ $x_{N+1}$ $y_{N+1}$ $x_{N+2}$ $y_{N+2}$ $:$ $:$ $x_{N+M}$ $y_{N+M}$

Output Format

Output the maximum possible radius of the smallest circle in one line.
The answer will be considered correct if the relative or absolute error is within $10^{-6}$.

Sample Input and Output

Sample Input #1

0 2
6 3
2 4

Sample Output #1

2.061552812808830

Sample Input #2

0 5
8 6
9 1
2 0
1 0
0 1

Sample Output #2

0.500000000000000

Sample Input #3

3 0
5 2 3
-1 0 2
2 -6 4

Sample Output #3

2.000000000000000

Sample Input #4

1 1
0 0 5
6 -3

Sample Output #4

1.708203932499369

Notes/Hints

Constraints

• $N$ is an integer between $0$ and $100$ inclusive.
• $M$ is an integer between $0$ and $100$ inclusive.
• $N + M \geq 2$.
• $x_i, y_i (1 \leq i \leq N + M)$ are integers between $-100$ and $100$ inclusive.
• $r_i$ is an integer between $1$ and $100$ inclusive.
• All given coordinates are distinct.
• The circles numbered $1, 2, 3, \cdots, N$ do not intersect, and no circle contains another.
• The circles numbered $N + 1, N + 2, N + 3, \cdots, N + M$ are not inside or on the circumference of the circles numbered $1, 2, 3, \cdots, N$.

Subtasks

Subtask $1$ [$70$ points]

• $N = 0$.
• $M = 2$.

Subtask $2$ [$140$ points]

• $N = 0$.

Subtask $3$ [$90$ points]

• No additional constraints.

见题面 Input 部分

见题面 Output 部分